This paper addresses the classical question: Is financial innovation beneficial to a society when markets are incomplete? The general answer given here is, on average, yes . The approach we employ is global analysis. To be precise, we consider the standard two-period exchange economy with uncertainty over S states of nature in the second period. There areI agents and J real assets, where J < S. It is shown that the set of Pareto pseudo-equilibria Φ p forms a submanifold (a subvector bundle) of the pseudo-equilibrium manifold Φ (vector bundle), whose codimension in Φ is (S - J)(I - 1). A simple economic intuition captured by this result is that, from a global point of view, more assets are beneficial to a society in the sense that more assets reduce the codimension of the set of Pareto equilibria and therefore enlarge its relative size in Φ. Therefore, on average , there is a greater chance of efficiency if we open new markets. Furthermore, the presence of the term (I - 1) indicates that the inefficiency cost of market incompleteness increases as the number of agents increases.